Statistics and Significant Figures

Using the same data set (1.00, 5.00, 7.00, 3.00, 5.00, 7.00, 8.00)

s = ( [(1.00 - 5,14)2 + (5.00 - 5,14)2 + (7.00 - 5,14)2 + (3.00 - 5,14)2 + (5.00 - 5,14)2

+ (7.00 - 5,14)2 + (8.00-5,14)2 ] / (7 - 1 )1/2

s = 2.48

Hence, a thorough expression of the average includes the standard deviation.

= 5.14 � 2.48

One way of indicating the uncertainty of an experimental measurement is rounding the result so it consists entirely of significant figures. So called significant figures include all the certain digits and the first uncertain digit.